Finite Group Databasebeta

← #1387×D73 #33000905

Subgroups — #1387×D73 #33000905

Order 18688.

614 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D73C211yesmaximal, characteristic
2C2×#108×D73C211yesmaximal, characteristic
3C2×#107×D73C211yesmaximal, characteristic
4#22608041C211yesmaximal, characteristic, complemented
5#22608040C211yesmaximal, characteristic, complemented
6#22608039C211yesmaximal, characteristic, complemented
7C73×#1387C211yesmaximal, characteristic, complemented
8C2×M16×D73—21no—
9C22×C8×D73C2211yescharacteristic
10C2×C4⋊C4×D73—21no—
11C2×#14556531C2211yescharacteristic
12C2×#14556530—21no—
13M32×D73—22no—
14M32×D73C414yescomplemented
15C2×C16×D73—21no—
16C2×#14556527C2211yescharacteristic
17C2×#14556526—21no—
18#108×D73—22no—
19#108×D73C414yescomplemented
20C2×#14556525C2211yescharacteristic
21C2×#14556524—21no—
22#107×D73—21no—
23#107×D73—21no—
24#107×D73C412yes—
25#107×D73C412yes—
26C2×M32×C73C2211yescharacteristic
27C2×#108×C73C2211yescharacteristic
28C2×#107×C73C2211yescharacteristic
29C22×C4×D73—41no—
30C22×C4×D73D411yescharacteristic
31C2×#11924012—21no—
32C2×#11924011—41no—
33M16×D73—24no—
34M16×D73—42no—
35C22×#10596831D411yescharacteristic
36C2×C8×D73—41no—
37C2×C8×D73C2×C412yes—
38C2×C8×D73C2×C411yescharacteristic
39C2×C8×D73C2×C411yescharacteristic
40C2×C8×D73C2×C412yes—
41C2×C8×D73D411yescharacteristic
42C2×C8×D73D411yescharacteristic
43C2×C8×D73D412yes—
44C2×C8×D73Q812yes—
45C2×C4⋊Dic73—21no—
46C2×#11924007—41no—
47C4⋊C4×D73—22no—
48C4⋊C4×D73—22no—
49C4⋊C4×D73—41no—
50C4⋊C4×D73—41no—
51#14556531—21no—
52#14556531C2×C412yescomplemented
53#14556530—24no—
54C2×#11924003—21no—
55C16×D73—24no—
56#14556527—21no—
57#14556527C2×C412yescomplemented
58#14556526—24no—
59#14556525—21no—
60#14556525C2×C412yes—
61#14556524—22no—
62#14556524—22no—
63C2×M16×C73—21no—
64C22×C8×C73C2311yescharacteristic
65C2×C4⋊C4×C73—21no—
66M32×C73—21no—
67M32×C73C2×C412yescomplemented
68C2×C16×C73—21no—
69#108×C73—21no—
70#108×C73C2×C412yescomplemented
71#107×C73—21no—
72#107×C73C2×C412yes—
73C23×D73SD1611yescharacteristic
74C22×Dic73—41no—
75C22×Dic73SD1611yescharacteristic
76C2×C4×D73—42no—
77C2×C4×D73—42no—
78C2×C4×D73—84no—
79C2×C4×D73C22⋊C412yes—
80C2×C4×D73C22⋊C411yescharacteristic
81C2×C4×D73C22⋊C411yescharacteristic
82C2×C4×D73C4⋊C412yes—
83C2×C4×D73D811yescharacteristic
84C2×C4×D73D811yescharacteristic
85C2×C4×D73SD1612yes—
86C2×C4×D73Q1612yes—
87#11924012—22no—
88#11924012—41no—
89#11924011—44no—
90C2×#10596831—41no—
91C2×#10596831C22⋊C411yescharacteristic
92C2×#10596831C22⋊C411yescharacteristic
93C2×#10596831C22⋊C412yes—
94C2×#10596831C4⋊C412yes—
95C8×D73—44no—
96C8×D73C4212yes—
97C8×D73C4212yes—
98C8×D73C22⋊C412yes—
99C8×D73C22⋊C412yes—
100C8×D73C4⋊C412yes—
101C8×D73C4⋊C412yes—
102C8×D73C4⋊C412yes—
103C8×D73C4⋊C412yes—
104C4⋊Dic73—22no—
105C4⋊Dic73—41no—
106#11924007—42no—
107#11924007—42no—
108#11924003—22no—
109C22×C4×C73—41no—
110C22×C4×C73C2×D411yescharacteristic
111M16×C73—22no—
112M16×C73—41no—
113C2×C8×C73—41no—
114C2×C8×C73C22×C411yescharacteristic
115C2×C8×C73C22×C411yescharacteristic
116C2×C8×C73C22×C411yescharacteristic
117C2×C8×C73C2×D411yescharacteristic
118C2×C8×C73C2×D411yescharacteristic
119C2×C8×C73C2×Q811yescharacteristic
120C4⋊C4×C73—22no—
121C4⋊C4×C73—41no—
122C16×C73—22no—
123C23×C73C2×SD1611yescharacteristic
124C22×D73—22no—
125C22×D73—22no—
126C22×D73#10211yescharacteristic
127C22×D73#10211yescharacteristic
128C22×D73#10312yes—
129C22×D73#10612yes—
130C2×C4×C73—42no—
131C2×C4×C73—82no—
132C2×C4×C73C2×C22⋊C411yescharacteristic
133C2×C4×C73C2×C22⋊C411yescharacteristic
134C2×C4×C73C2×C4⋊C411yescharacteristic
135C2×C4×C73C2×D811yescharacteristic
136C2×C4×C73C2×SD1611yescharacteristic
137C2×C4×C73C2×Q1611yescharacteristic
138C2×Dic73—42no—
139C2×Dic73—82no—
140C2×Dic73#10211yescharacteristic
141C2×Dic73#10211yescharacteristic
142C2×Dic73#10312yes—
143C2×Dic73#10612yes—
144C4×D73—84no—
145C4×D73—84no—
146C4×D73#9512yes—
147C4×D73#9512yes—
148C4×D73#10212yes—
149C4×D73#10212yes—
150C4×D73#10312yes—
151C4×D73#10312yes—
152C4×D73#10712yes—
153C4×D73#10712yes—
154C8×C73—42no—
155C8×C73C2×C4211yescharacteristic
156C8×C73C2×C22⋊C411yescharacteristic
157C8×C73C2×C4⋊C411yescharacteristic
158C8×C73C2×C4⋊C411yescharacteristic
159#10596831—42no—
160#10596831#9512yes—
161#10596831#9512yes—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73C2×#10211yescharacteristic
165C22×C73C2×#10311yescharacteristic
166C22×C73C2×#10611yescharacteristic
167C2×D73—21no—
168C2×D73—21no—
169C2×D73—24no—
170C2×D73—24no—
171C2×D73#34012yes—
172C2×D73#34012yes—
173C2×D73#36112yes—
174C2×D73#36212yes—
175C4×C73—82no—
176C4×C73C2×#9511yescharacteristic
177C4×C73C2×#10211yescharacteristic
178C4×C73C2×#10311yescharacteristic
179C4×C73C2×#10711yescharacteristic
180Dic73—82no—
181Dic73#34012yes—
182Dic73#34012yes—
183C2×#1387—731nomaximal, Sylow
184C2×C73—21no—
185C2×C73—21no—
186C2×C73C2×#34011yescharacteristic
187C2×C73C2×#36111yescharacteristic
188C2×C73C2×#36211yescharacteristic
189D73—22no—
190D73#138714yesdirect product factor
191C22×M32—731no—
192C22×#108—731no—
193C22×#107—731no—
194#1387—731no—
195#1387—731no—
196#1387—731no—
197#1387D7311yescharacteristic, direct product factor
198C73C2×#138711yescharacteristic, complemented, Sylow
199C22×M16—1461no—
200C23×C8—731no—
201C22×C4⋊C4—1461no—
202C2×M32—731no—
203C2×M32—734no—
204C2×M32—1461no—
205C2×M32—1462no—
206C2×M32C2×D7311yescharacteristic
207C22×C16—1461no—
208C2×#108—731no—
209C2×#108—734no—
210C2×#108—1462no—
211C2×#108—1461no—
212C2×#108C2×D7311yescharacteristic
213C2×#107—731no—
214C2×#107—732no—
215C2×#107—732no—
216C2×#107—1461no—
217C2×#107—1461no—
218C2×#107—1461no—
219C2×#107C2×D7311yescharacteristic
220C23×C4—2921no—
221C23×C4—731no—
222C2×M16—21no—
223C2×M16—2921no—
224C2×M16—2922no—
225C2×M16—1464no—
226C2×M16—1461no—
227C22×C8—2921no—
228C22×C8—731no—
229C22×C8—731no—
230C22×C8—731no—
231C22×C8—732no—
232C22×C8—732no—
233C22×C8—731no—
234C22×C8—731no—
235C22×C8—732no—
236C22×C8—732no—
237C22×C8C22×D7311yescharacteristic
238C2×C4⋊C4—21no—
239C2×C4⋊C4—2921no—
240C2×C4⋊C4—2921no—
241C2×C4⋊C4—2921no—
242C2×C4⋊C4—1462no—
243C2×C4⋊C4—1462no—
244C2×C4⋊C4—1461no—
245M32—21no—
246M32—732no—
247M32—1464no—
248M32—1461no—
249M32C4×D7312yescomplemented
250C2×C16—21no—
251C2×C16—1464no—
252C2×C16—1461no—
253#108—21no—
254#108—732no—
255#108—1464no—
256#108—1461no—
257#108C4×D7312yescomplemented
258#107—21no—
259#107—732no—
260#107—1462no—
261#107—1462no—
262#107—1461no—
263#107C4×D7312yes—
264C24—731no—
265C22×C4—41no—
266C22×C4—2922no—
267C22×C4—2922no—
268C22×C4—2921no—
269C22×C4—5844no—
270C22×C4—731no—
271C22×C4—731no—
272C22×C4—731no—
273C22×C4—732no—
274C22×C4—732no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—732no—
278C22×C4—732no—
279C22×C4D4×D7311yescharacteristic
280M16—22no—
281M16—41no—
282M16—2924no—
283M16—2921no—
284M16—1462no—
285C2×C8—41no—
286C2×C8—2924no—
287C2×C8—2921no—
288C2×C8—731no—
289C2×C8—731no—
290C2×C8—732no—
291C2×C8—732no—
292C2×C8—732no—
293C2×C8—732no—
294C2×C8—732no—
295C2×C8—732no—
296C2×C8—732no—
297C2×C8—732no—
298C2×C8—732no—
299C2×C8—732no—
300C2×C8C2×C4×D7311yescharacteristic
301C2×C8C2×C4×D7311yescharacteristic
302C2×C8C2×C4×D7311yescharacteristic
303C2×C8D4×D7311yescharacteristic
304C2×C8D4×D7311yescharacteristic
305C2×C8Q8×D7311yescharacteristic
306C4⋊C4—22no—
307C4⋊C4—41no—
308C4⋊C4—2922no—
309C4⋊C4—2922no—
310C4⋊C4—2921no—
311C4⋊C4—1462no—
312C16—22no—
313C16—1462no—
314C23—731no—
315C23—732no—
316C23—731no—
317C23—732no—
318C23—1462no—
319C23—1462no—
320C23SD16×D7311yescharacteristic
321C2×C4—42no—
322C2×C4—82no—
323C2×C4—2922no—
324C2×C4—5844no—
325C2×C4—5844no—
326C2×C4—5842no—
327C2×C4—732no—
328C2×C4—731no—
329C2×C4—731no—
330C2×C4—732no—
331C2×C4—732no—
332C2×C4—732no—
333C2×C4—732no—
334C2×C4—732no—
335C2×C4—732no—
336C2×C4—732no—
337C2×C4—732no—
338C2×C4—732no—
339C2×C4C22⋊C4×D7311yescharacteristic
340C2×C4C22⋊C4×D7311yescharacteristic
341C2×C4C4⋊C4×D7311yescharacteristic
342C2×C4D8×D7311yescharacteristic
343C2×C4SD16×D7311yescharacteristic
344C2×C4Q16×D7311yescharacteristic
345C8—42no—
346C8—2922no—
347C8—732no—
348C8—732no—
349C8C42×D7311yescharacteristic
350C8C22⋊C4×D7311yescharacteristic
351C8C4⋊C4×D7311yescharacteristic
352C8C4⋊C4×D7311yescharacteristic
353C22—21no—
354C22—21no—
355C22—732no—
356C22—732no—
357C22—732no—
358C22—732no—
359C22—1464no—
360C22—1464no—
361C22—1461no—
362C22—1461no—
363C22#102×D7311yescharacteristic
364C22#103×D7311yescharacteristic
365C22#106×D7311yescharacteristic
366C4—82no—
367C4—5842no—
368C4—732no—
369C4—732no—
370C4#95×D7311yescharacteristic
371C4#102×D7311yescharacteristic
372C4#103×D7311yescharacteristic
373C4#107×D7311yescharacteristic
374C2—21no—
375C2—21no—
376C2—734no—
377C2—1462no—
378C2#340×D7311yescharacteristic
379C2#361×D7311yescharacteristic
380C2#362×D7311yescharacteristic
subgroupG/H
centerC22#102×D73
commutatorC8×C73C2×C42
FrattiniC22×C8C22×D73
FittingC73×#1387C2
socleC22×C73C2×#102
prime radicalC23×D73SD16
cosocleC22×C8×C73C23
hypercenter#1387D73
hypocenterC73C2×#1387
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1387

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #22608041C2semidirect
5. #22608040C2semidirect
6. #22608039C2semidirect
7. C73×#1387C2semidirect
14. M32×D73C4semidirect
19. #108×D73C4semidirect
52. #14556531C2×C4semidirect
57. #14556527C2×C4semidirect
67. M32×C73C2×C4semidirect
70. #108×C73C2×C4semidirect
190. D73#1387direct (N × H)
197. #1387D73direct (N × H)
198. C73C2×#1387semidirect
249. M32C4×D73semidirect
257. #108C4×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×M32×D732
C2×#108×D732
C2×#107×D732
#226080412
#226080402
#226080392
C73×#13872
C2×#138773